Hey Pacmeng, hope these following links can be of some assistance to you. Pretty sad that a 3 day old thread has only gotten one response, but I'll give it a shot.
The following is a server verification error fix. Not sure if it's anything related to what you're experiencing, but it's definitely worth trying.
https://support.steampowered.com/kb_...php?p_faqid=47
This is a more common one, and is similar to the "No steam login" error. It will ask you to delete 3 files that recreate themselves from scratch once you launch Counterstrike again. Somehow those files have become corrupt and need to be "refreshed".
https://support.steampowered.com/kb_...php?p_faqid=30
This is another one that might help.
https://support.steampowered.com/kb_...1817-RTSK-8917
After searching through the site a little more I think I found the solution to your exact problem.
https://support.steampowered.com/kb_...7579-RPSX-6098
Good luck bro. Always happy to help